the valuation of future cash flows an actuarial issues paper

79 Pages·1999·0.2 MB·English

THE VALUATION OF FUTURE CASH FLOWS
AN ACTUARIAL ISSUES PAPER
By Sam Gutterman, FSA, FCAS
March 19, 1999
THE VALUATION OF FUTURE CASH FLOWS
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TABLE OF CONTENTS
Section Page
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2. Valuation models
a. Approaches to valuation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
b. Major components of a present value model . . . . . . . . . . . . . . . . . . . . 8
c. A set of cash flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
d. Audiences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
e. Use of valuation models and accounting rules . . . . . . . . . . . . . . . . . . . 19
f. Whose cash flows? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
g. Recognition of present values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3. Risk
a. The concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
b. Whose viewpoint? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
c. Application of risk adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
d. Methodologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
e. Risk management . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
4. The discount rate
a. Time value of money . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
b. Application to negative and positive cash flows . . . . . . . . . . . . . . . . . 57
c. Discount rate structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
d. Nominal or real discount rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
e. Entity’s own default risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
f. Locked in or dynamically adjusted . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
g. Taxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
5. Other necessary items
a. Applications. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
b. Criteria to judge usefulness of valuation results . . . . . . . . . . . . . . . . . . 66
c. Disclosure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
d. Certain technical issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
6. Executive Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Definitions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
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1. INTRODUCTION
The value of a set of future cash flows (valuation) can serve many purposes, including the
allocation of scarce resources, determination of the price at which a product will be
offered (often supplemented with relevant information concerning the market or vice
versa), and the estimation of the value of assets, obligations, or companies. The objective
of such a valuation is to determine, to the extent possible, the economic value of one or
more sets of cash flows or the relative economic differences between the value of
alternate sets of estimated cash flows. Such valuations are particularly important in
actuarial practice.
The value or worth of a set of cash flows can be determined through an analysis of the
cash flows themselves, in addition to reflecting the time value of money and cost of risk.
This value can be demonstrated by the actual price at which a transaction occurs; such a
transaction can be influenced by additional factors, such as the environment in which a
transaction occurs or in some cases the particular buyer or seller involved. Depending on
the situation, value may be developed with respect to either a particular decision-maker or
a general audience in mind.
Many believe that when attempting to determine the value of a set of cash flows, reliance
should be placed only on the price at which two parties are willing to exchange ownership
(market price) or the market price of comparable cash flows. However, in many cases in
which an assessment of value is needed, the only markets in which comparable cash
flows are traded are either thin, undeveloped, or volatile; in other cases there may be no
such market at all. In these cases, such market prices may not be readily determinable,
available, or reliable.
The objective of this paper is to present and discuss the principles underlying the
determination of the value of a set of future cash flows. This topic is central to actuarial
practice. Currently, alternative points of view are held on several of the significant issues
involved; an attempt is made to present some of them. This paper is intended to serve as
a broad overview of this topic and to encourage further discussion of the issues involved.

The original title of this paper was “Present Value of Future Cash Flows”. It was
changed after I became convinced that the application of present values can best be
viewed in a wider valuation context. It is appropriate that the widely used approach of
present values, as used by actuaries and other financial professionals, be discussed in
terms of its wide applications and in relation to valuations conducted on a market-based
approach.

Standards of practice that an actuary should follow in determining such present values
will not be explicitly addressed here, although in some cases, some factors that should be
taken into account are mentioned. Such standards include the considerations that should
be reflected in applying these principles.
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Acknowledgements. A number of actuaries provided constructive suggestions that have
served to improve this paper, too numerous to mention here. However, I would like to
specifically mention Chris Daykin, Jim Hickman and Francis Ruygt for their comments.
In addition, assistance and encouragement was received by a number of members of the
IASC Insurance Accounting Standards Committee of the International Actuarial
Association (IAA). I would like to thank all who provided me with assistance in
developing the ideas expressed here.

My views on this subject have evolved substantially as I have studied the issues involved.
I expect them to continue to evolve. An enhanced version of this paper is possible. As
such, I hope that this paper evokes an ongoing dialogue and resolution to some of the
substantive and controversial issues discussed here. Many of the issues addressed here
require further discussion and rigorous analysis.
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2. VALUATION MODELS

2a. Approaches to valuation

Value incorporates both objective and subjective components. It is typically easier to
estimate and validate the objective aspects, while in order to determine subjective aspects
it may be necessary to observe the results of real experiments. Techniques to quantify
both aspects have evolved and improved over time. The most appropriate method,
considerations and judgment to be applied in the development of an actuarial assessment
of value may vary depending upon the objectives and audience for which the assessment
is being conducted.

Value can be viewed in several ways. One approach is to base it on an estimate of the
cash flows involved, while another is to base it on some benchmark indicators that can be
trusted to fairly demonstrate value. Estimates of values typically involve the application
of a model, a representation of reality, generally based on a set of simplifying
assumptions. Such a model may be as simple as an observation of comparable market
prices or as complicated as an actuary or financial economist can make it. Models are
needed both to supplement areas in which insufficient information is available and to
enable a decision-maker to better understand the dynamics of financial conditions and
effects. In fact, information is a key element, because the less that is known, the greater
the uncertainty, the wider the likely range between bid and asked price and in turn risk.
A model is often used to develop estimates of value. A mathematical model is a
depiction of reality expressed in mathematical terms. Actuaries study the cash flows
reflecting the real world, rather than an idealized world. Models are necessary because the
real world rarely permits experimentation that studies the effect of one variable at a time.
It is important for actuaries to strive to reflect statistical, probabilistic, behavioral and
economic principles. However, although it is necessary for the theory upon which the
model is based to be internally consistent, it is more important that it leads to useful
results. Sometimes theory, depending on the assumptions used, leads to naïve
approximations that need to be adjusted on the basis of experience.

One family of approaches to valuation develops estimates of future cash flows on the
basis of a cash flow model from which cash flows are estimated, from which estimates of
value are derived, assessed as of a particular point in time (sometimes referred to as a
discounted cash flow approach). This value is equal to the expected present value
(sometimes referred to as actuarial present values) of a set of future cash flows associated
with a particular asset, financial instrument, obligation, product, project, or company. A
present value model represents an important method of determining the value of a set of
future cash flows. It is often assumed that people generally act in a rational manner
anticipated by the concepts underlying present value models, although the risks associated
with deviations from this assumption should be recognized.
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Other approaches represent variations of present value models, reflecting refinements or
amplifications, for example, the use of an option-pricing model for evaluating the cost or
benefit associated with embedded options.
The estimation of the value of these future cash flows is central to actuarial practice.
Enhanced technology and widespread use of applicable techniques have enabled
increased use of the concepts underlying these approaches. Hopefully, this trend should
continue.
The combined effect of individual cash flows can be represented in the form of cash or
cash equivalents and can be either:
• Positive, representing an asset involving current cash or its equivalent or the
expectation of receipt of a future cash flow or

• Negative, representing an obligation to pay cash or its equivalent.

Assets and obligations consist of one or more such cash flows. It is useful to begin the
discussion of the valuation of these financial elements in terms of their component cash
flows to better understand their combination.

Another family of approaches often used to estimate value relies on a market-based
approach. A market is an arrangement for facilitating transactions involving goods by
matching buyers and sellers often carried out through the exchange of money or its
equivalent. This paper primarily focuses on financial markets, in which the goods traded
consist primarily of sets of cash flows (economic goods). An efficient market (one in
which perfect competition exists) is one with complete and accurate information available
to both buyers and sellers in a voluntary situation (no forced sales or purchases), typically
with many buyers and sellers. In such a market, the expected value of market price is
uniquely defined as of a particular point in time. In such a market, the opportunities for
arbitrage profits are limited.

The relationship between present values and market prices is important to recognize.
Several definitions may help:

• Market price. The transaction price of a set of future cash flows (possibly combined
in the form of a financial instrument, other asset, obligation, or even an entire
company) which is traded between two or more parties when sold in a given market.
Except in the cases of an efficient market (there are few of these around) or the set of
cash flows analyzed is a commodity in which transaction prices are consistent, a
market price has to be used with caution to value a similar set of cash flows, as it
tends to change over time and between different sets of buyers and sellers. Even in an
efficient market, transaction costs such as securitization fees or taxes may be incurred
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that would result in the market price as recognized by the buyer and seller being
different. By their nature, market prices are marginal in nature, that is, they reflect the
valuation of the marginal or last investor prior to valuation. Typically if such prices
are used as comparables, a prospective value is desired.
• Market value. This is an estimate of the market price, and can serve as a surrogate for
the market price if there had been an equivalent transaction in a market. In an
efficient market, the expected value of a market price is the market value and is
uniquely defined as of a specific point in time. If a market is inefficient, it is the price
for a set of cash flows that would have been arrived at if an efficient market had
existed.
• Present value. This represents an estimate of the underlying value of a set of future
cash flows. It is the value of future cash flows taken from a particular point of view at
a particular point in time. Some believe that present values serve as a useful surrogate
for fair values (while others believe that market values are samples from a population
of possible present values).
• Fair value. This is defined as the amount for which a set of cash flows could be
exchanged or settled in an arm’s length transaction between informed and willing
parties, other than in a forced sale or liquidation. This amount is derived by applying
the principles, which are perceived to underlie the market value of the set of cash
flows if it had been currently traded in an efficient market. This concept encompasses
an estimate of the market value on a current or prospective basis, whether or not a
market for the economic good exists, or a present value representing a fundamental
value if not. It could also be viewed as being one of a family of present value
approaches, whose assumptions are based on the assessment of a relevant market if it
exists and a hypothetical market if it does not. It should reflect expected transaction
costs.

Financial economists have generally focused on assets or liabilities that can be easily
traded (or securitized). Their theories typically reflect a frictionless world, one that is
useful for many purposes, but generally don’t exist. Thus, market values are a good
starting point and in many cases are sufficient. However, fair value needs to be realistic,
as it should take into account such aspects as transaction costs.

In a non-efficient market, differences between market value and present value may arise.
These differences may be due to such factors as market imperfections, different risk
preferences between buyers and sellers, and variation in perceptions of market risk. Even
in relatively “efficient” markets, imperfections exist (although the following quote from
the 24 January 24 1998 edition of the Economist relates to the volatile situation in East
Asia, it can equally apply to any financial market):
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“But real financial markets are more complex than the textbook models. Investors
are erratic, swayed by waves of excessive optimism followed by waves of
excessive pessimism. And it is impossible to eliminate moral hazard, which
causes people to take excessive risks in the expectation that a central bank or the
IMF will bail them out when things go wrong. These factors can mean that
market forces do not allocate capital perfectly around the world.”

Another quote relates to one of the more efficient markets, the New York Stock
Exchange. According to Robert Froelich, chief investment strategist for Scudder Kemper
Investments on 27 May 1998: “We’re going to have to get used to dramatic swings,
because the market’s not trading on fundamentals now. It’s an emotional market.” If this
is the case in the situation cited, the determination of value to be recognized must
regularly weigh both the relative importance of (1) market determination and (2)
underlying fundamentals of a set of cash flows.

This difference can be referred to as a market discount (if the market value is less than the
present value, or a market premium if the market value is greater than the present value).
Present value models can thus be used to estimate value when an appropriate market
value is not readily available, indicating whether to buy or sell a set of cash flows at a
given price, or comparing the relative value of two or more sets of cash flows. One
approach is then to combine the two general methods, with a present value model used to
estimate the “fundamental” value and a market-related approach to estimate the market
discount or premium.

One judgment of the difference between fundamental and market-based pricing is
revealed by Larry Summers1 when he noted that empirical tests of the efficient market
hypothesis do not generally address whether prices are equal to fundamental values and
concludes that frequent divergence of prices and such values by over thirty percent is
consistent with available empirical data. This difference is due in part to the fact that
most markets respond not only to information, but also to opinion and emotion, both
subject to human bias. These can change often and by a significant amount.

Although it appears that, due to a limited number of efficient markets, market value may
not be of much use. On the contrary, such values should be derived if possible. In many
cases they form the basis of best estimates of value available to a marginal, perhaps
typical investor.

Other forms of market-based valuation methods exist. One reflects historical costs (that
are based on a previous market price or market value). Various approaches can be used
to develop a current value reflecting such a historically based cost, including interest
methods (e.g., amortization of a bond purchased at a discount) and depreciation methods

1 “Does the Stock Market Rationally Reflect Fundamental Values?”, Journal of Finance, Vol. XLI, No. 3,
July, 1996
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(e.g., regular reduction in value based on a rule, typically for properties). These methods
are not necessarily related to an assessment of future cash flows.

Another related value estimation method is net realizable value upon settlement. Time
becomes important in this approach, because the value at the current time (market value
or current settlement value) may be different than if a set of cash flows were settled
sometime in the future.

One can also view a market price as a sample of fair values. In the case of an efficient
market, the value of all such samples would be identical. To the extent that differences in
market prices result only from statistical fluctuations, sampling theory might be used to
study these values based on historical observations.

2b. Major components of a present value model

The present value of future cash flows is based on three components: estimates of the
amount of the cash flows resulting from the application of a present value model,
estimates of their timing, and adjustments made to the estimates by means of one or more
discount factors. The estimates made as of a specific valuation date often involve
possible future cash flows that are of uncertain amount and timing. As a result, an
actuary will consider the range of possible values and not simply a single set of selected
cash flows and a single set of discount rates applied to a stream of future cash flows, even
if such sets are the most likely ones. The way in which this range is reflected and
adjustments made to the set of expectations and uncertainties associated with these cash
flows, form the basis of the construction and application of the present value model,
applied on the basis of actuarial judgment.

Three fundamental principles of actuarial science underlie the present value model --
expected value of future cash flows, time preference and risk aversion.

• Expected value of future cash flows. The components of certain sets of cash flows
(or their monetary equivalents) may be analyzed separately in terms of their actuarial
risk variables: incidence (or frequency), severity (or average size), and timing.
Depending on the types of cash flows involved, it may be desirable to estimate future
cash flows based on these separately or in combination. In developing estimates, it is
necessary to analyze a range of possible values, along with corresponding
probabilities of occurrences likely in the future. These probabilities can either be
developed on an objective or subjective basis, the latter typically used if the necessary
information or experience is unavailable to develop objective estimates or to
supplement experience.
An expected or mean value for the future cash flows would then be developed.
Mathematically, an expected value is the probability-weighted measure assigned to
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the range of uncertain amounts or scenarios. Alternative measures could include the
median (the middle value of a set of possible results) or the mode (most likely value).
In some cases, it may be tempting to select what some refer to as the most likely
value; this value which represents the mode of a probability distribution, in some
cases may be significantly different than the mean value of the distribution.
Alternative approaches may be used; for example, the average of a high and low
estimate or mean value of each experience assumption that would not necessarily
result in the mean value of total value.
In some cases, the mean value may be a hypothetical one; that is, it may be unlikely or
even impossible to achieve, as it may be between two possible values. An example is
a situation in which a value could be either $1,000 or $4,000, with the former being
twice as likely as the latter. The mean would be $2,000 (2/3 of $1,000 + 1/3 of
$4,000), with a most likely value of $1,000. Although the $2,000 value is not a
possible result, it is a more appropriate value to assign to the situation.
In other cases, appropriate adjustments are needed (for example, for certain decisions
a few extreme outcomes with very low probabilities may be possible; in such a case a
result closer to the median or a calculation applying a smaller weight to these extreme
values may be appropriate). Judgment is important to determine if these alternatives
are preferable. In other cases, the development of an estimate of the mean of a set of
cash flows is complicated, for example for long-term contracts such as life insurance.

If all real phenomena were only like the tossing of a coin, and the coin could always
be tossed under the same circumstances many times, these values would also be
similar; however, experimental evidence most likely will not bear out such a
simplifying assumption in which a normal distribution with known parameters.
Although most actual distributions are typically not symmetrical, it is usually deemed
sufficient to use the mean or expected value. In addition, it can be important to
recognize the impact of lack of symmetry and non-linearity of the distributions and
risk (see risk preference below) associated with uncertain future cash flows in the
other two components of value.

If a set of cash flows is to be bought or sold, it is appropriate to reflect expected
associated transaction costs that may be considerable. Since such costs may vary
depending on how or when such a transaction occurs, the specific decision being
addressed would affect value placed on the cash flows, or alternatively, a range of
possible actions.

• Time preference (time value of money). Money and time have value because they
are scarce resources. This can be seen from the actions of lenders who demand and
borrowers who forgo additional money for its use over time. A given amount of